Internet

Web browser

Firefox is free software developed by Mozilla. It is highly extensible via addons and included as the default browser in many Linux distributions. It is often criticized on /g/ and /tech/ as "SJWfox" because of some Mozilla developers outspoken campaigns on social and political issues.

QupZilla is a FOSS web browser, built on the Qt and QtWebEngine (based on Chromium's rendering engine) frameworks. It supports extensions, ships out of the box with AdBlock, Mouse Gestures, GreaseMonkey, Speed Dial, Click2Flash, and more. It provides seamless integration with most desktop environments, and has several other distinguishing features. QupZilla is licensed under GPLv3.

Opera is a proprietary web browser that has pioneered open web standards for over two decades. It is notable for being the first web browser to sport a tabbed interface. It is developed and maintained by Opera Software.

Chromium is the developer version of Google Chrome. Its tracking features can be easily disabled. Although it is free and open source software, its code is not as well audited as Firefox.

Otter Browser is a FOSS web browser that aims to recreate the best aspects of the classic Opera (12.x) UI using Qt5.

SeaMonkey is a continuation of the Mozilla suite. Unlike most modern web browsers, it is an Internet suite, complete with bundled programs for email, IRC, and web design. It is compatible with most Firefox add-ons.

Tor Browser (formerly known as Tor Browser Bundle) is a package of a modified Firefox extended support release, NoScript, HTTPS-Everywhere, Tor, TorButton and TorLauncher. It automatically routes traffic through the Tor network and deletes history and cookies when closed.

RetroShare is an open source decentralized communication platform. It provides secure chat, photo and video sharing using OpenPGP to authenticate peers and OpenSSL to encrypt all communication.

Internet Relay Chat (IRC)

HexChat is a popular replacement for the XChat IRC client, a client which offered a free binary for Linux but charges money for the Windows version. HexChat is a continuation of XChat and makes both its source code and binaries available to users of all platforms it's created for. Like its parent software, HexChat is licensed under the GNU GPL. It includes all the basic features one would need, and can be ideal both for new users and IRC veterans.

BitTorrent (BT)

Transmission is a lightweight torrent client with support for blocklists.

qBittorrent is a libtorrent-based BitTorrent client. According to its developers, the aim of the client is to provide a free software alternative to µTorrent. There's also a daemon version called Qbittorrent-nox.

Deluge is a libtorrent-based BitTorrent client. It is highly extensible via its plug-ins system. Deluge is notable for having originated the particular method of protocol encryption that is currently in use by every major BitTorrent client.

Terminal

qBittorrent-nox is an advanced command-line Bittorrent client written in C++ / Qt4, using the libtorrent-rasterbar library by Arvid Norberg. qBittorrent-nox aims to be a good alternative to other command line bittorrent clients and provides features similar to popular graphical clients. qBittorrent-nox is fast, stable, light and it supports unicode. It also comes with UPnP port forwarding / NAT-PMP, encryption (Vuze compatible), FAST extension (mainline) and PeX support (uTorrent compatible).

Deluge-Console is an ncurses interface for Deluge that generally comes bundled with the main GUI client.

File Transfer Protocol (FTP)

Other

Text

Word Processing

Bean is a small, easy-to-use word processor that is designed to make writing convenient, efficient and comfortable. Bean is lean, fast and uncluttered. It starts up quickly, has a live word count, and is easy on the eyes. Also, Bean is available free of charge.

Editing

Final Cut Pro X Expensive, but powerful and easy to use. (Still cheaper than Adobe though)

Conversion/Ripping

Handbrake is a free and open source video transcoder with an easy to use GUI. It can rip and convert a variety of video formats, but can not break DVD or Blu-ray copyright protection.

MakeMKV can convert video from proprietary (and usually encrypted) discs into a set of MKV files, preserving most information but not changing it in any way. It can instantly stream decrypt video without intermediate conversion and decrypt Blu-rays and protected DVDs.

Utilities

Archiving

7zip is a free and open source file archiver developed in C++ by Igor Pavlov. Its primary feature is lossless compression in the 7z format, based upon the Lempel–Ziv–Markov chain algorithm. In addition to the handful of formats it is capable of creating new archives in, 7zip can retrieve files from archives in virtually any format that one is likely to encounter. Only Windows binaries are provided on the site, but OS X and Linux binaries are available.